The surface area of a square pyramid is 116 inches squared and the total area of the pyramid's four triangular faces is 80 inches squared. What is the length of one of the sides?
Let's denote the length of one side of the square base as "s" and the height of the pyramid as "h".
The surface area of a square pyramid is calculated using the formula:
Surface Area = Base Area + (1/2 * Perimeter of Base * Slant Height)
Given that the surface area of the square pyramid is 116 inches squared and the total area of the pyramid's four triangular faces is 80 inches squared:
116 = s^2 + (1/2 * 4s * h)
80 = 4 * (1/2 * s * h)
Now we need to solve this system of equations to find the values of "s" and "h".
From the second equation, we can simplify to:
80 = 2s * h
80 = 2sh
Rearranging:
h = 80 / (2s)
h = 40 / s
Now we substitute h=40/s in the first equation:
116 = s^2 + (1/2 * 4s * 40/s)
116 = s^2 + 80
Rearranging and simplifying:
s^2 = 36
s = 6
Therefore, the length of one of the sides of the square base of the pyramid is 6 inches.